Apparatus and method for imager device color calibration using spectral light source

ABSTRACT

A method and apparatus for color calibrating an imager device is disclosed. The imager device is subjected to a plurality of light sources. Color channel responses are obtained from the imager device and the color calibrating coefficients are determined.

This application is a continuation of U.S. application Ser. No.09/102,875 filed Jun. 23, 1998 and issued Mar. 20, 2001 as U.S. Pat. No.6,205,244.

BACKGROUND OF THE INVENTION

(1) Field of the Invention

The present invention is generally related to the verification andcalibration of color as well as corrective adjustments for an imagingdevice.

(2) Background Information

Color is basically what the human visual system perceives on receivingvarious wavelengths of light that have reflected off objects. This colorrecognition is also known as the spectral sensitivity of the humanvisual system. To express the perceived colors numerically, many methodshave been developed of which one of them is the XYZ tristimulus valuesas developed by an international organization known as “CommissionInternationale de I'Eclairge” (CIE). The XYZ tristimulus values arebased on the theory that the human visual system possesses receptors forthree primary colors red, green, and blue and that all the colorsperceived are mixtures of these three primary colors.

FIG. 1 illustrates the spectral sensitivity corresponding to the humanvisual system in terms of XYZ tristimulus values. Ideally, if imagerdevice response channels were to exactly duplicate the XYZ tristimulusvalues, in theory, that imager device could be capable of exactlyduplicating the colors seen by the human visual system. However, due tothe complexities involved in producing such an imager device, it is notpractical to exactly duplicate the XYZ tristimulus values.

FIG. 2 illustrates an exemplary red, green and blue response of animager device. It is desirable to transform the response to be asclosely correlating as possible to the XYZ tristimulus values so thatthe imager device may channel outputs that closely correspond to thecolor seen by the human visual system. This is the function of colorcalibration that is performed on the imager device.

The function of the color calibration is to find a color calibratingmatrix (e.g., a 3×3 matrix) that brings the response of the image sensoras close as possible (i.e., least squares error) to that of the XYZtristimulus values. An exemplary method of determining the colorcalibrating 3×3 matrix is to take several reflective color targets ofknown XYZ tristimulus values such as a rendition chart having theMacbeth Colorchecker® targets available from Macbeth/KollmorgenInstruments Corporation in New Windsor, N.Y., that represent twenty-fourcolors and generally depict the colors in various regions of the colorspace. By taking the corresponding red, green and blue (RGB) valuesgenerated by the image device, a calibrating matrix that closelyrepresents the XYZ tristimulus values of the targets is found.Mathematically, the transformation may be represented as follows:

Using the imager device to be calibrated, twenty-four color targetshaving known X Y Z tristimulus target values are read (measured) by theimager to produce responses in the imager. From these responses, theimager generates the corresponding RGB values. Note that each X Y Ztristimulus values for the color targets are known. The measured RGBvalues are loaded into a measured data matrix (MEAS), an example being:$\begin{matrix}{{Target}\mspace{14mu} 0} \\{{Target}\mspace{14mu} 1} \\{{Target}\mspace{14mu} 2} \\{{Target}\mspace{14mu} 3} \\\vdots \\{{Target}\mspace{14mu} 22} \\{{Target}\mspace{14mu} 23}\end{matrix}\begin{matrix}R_{0} & G_{0} & B_{0} \\R_{1} & G_{1} & B_{1} \\R_{2} & G_{2} & B_{2} \\R_{3} & G_{3} & B_{3} \\\vdots & \vdots & \vdots \\R_{22} & G_{22} & B_{22} \\R_{23} & G_{23} & B_{23}\end{matrix}$

The relationship between the RGB values and the XYZ tristimulus valuescan be represented by the equation: $\begin{bmatrix}X \\Y \\Z\end{bmatrix} = {\left\lbrack {3 \times 3} \right\rbrack\begin{bmatrix}R \\G \\B\end{bmatrix}}$

The 3×3 color calibrating matrix can be further specified as:$\left\lbrack {3 \times 3} \right\rbrack = \begin{bmatrix}M_{11} & M_{12} & M_{13} \\M_{21} & M_{22} & M_{23} \\M_{31} & M_{32} & M_{33}\end{bmatrix}$

Where M₁₁, . . . , M₃₃ are the desired color calibrating coefficients ofthe color calibrating matrix.

Thus, the color calibrating coefficients are computed as follows:$\begin{bmatrix}M_{11} \\M_{12} \\M_{13}\end{bmatrix} = {{\left( {{MEAS}^{T} \cdot {MEAS}} \right)^{- 1} \cdot {{{MEAS}^{T}\begin{bmatrix}X_{0} \\X_{1} \\\vdots \\X_{23}\end{bmatrix}}\begin{bmatrix}M_{21} \\M_{22} \\M_{23}\end{bmatrix}}} = {{\left( {{MEAS}^{T} \cdot {MEAS}} \right)^{- 1} \cdot {{{MEAS}^{T}\begin{bmatrix}Y_{0} \\Y_{1} \\\vdots \\Y_{23}\end{bmatrix}}\begin{bmatrix}M_{31} \\M_{32} \\M_{33}\end{bmatrix}}} = {\left( {{MEAS}^{T} \cdot {MEAS}} \right)^{- 1} \cdot {{MEAS}^{T}\begin{bmatrix}Z_{0} \\Z_{1} \\\vdots \\Z_{23}\end{bmatrix}}}}}$

A matrix may be thought of as a rectangular column and row array ofnumeric or algebraic quantities subject to mathematical operations. Atranspose is a matrix formed by interchanging the rows and columns of agiven matrix. In the above expression, MEAS^(T) refers to the transposeof MEAS matrix. ( )⁻¹ denotes an inverse. Further, Xn, Yn, Zn are XYZtristimulus values of the respective targets n.

The least-squares method is a method to obtain the best values (the oneswith least error) of unknown quantities that are supposed to satisfy asystem of linear equations, such as may be expressed by matrices. Fromabove, the color calibrating coefficients M₁₁, . . . , M₃₃ are selectedto provide the minimized least squares error that corresponds to thebest fit for mapping the measured RGB values of the imager device intothe known XYZ tristimulus values of the color targets. It may not beimmediately apparent why the coefficients obtained through this methodwould provide the least squares error and further discussion can befound in Box, Hunter and Hunter, “Statistics for Experimenters” (JohnWiley and Sons, New York, 1978) at page 498–502. It is desirable thatthe coefficient values be calculated and stored with a minimum of threesignificant digits of accuracy. Note that as long as the properluminance is provided against the rendition chart targets (or targetchips), the magnitudes of the coefficients are not important but onlythe ratios between the coefficients. Thus, the matrices:$M = \begin{pmatrix}16.645 & 7.013 & 1.253 \\6.997 & 17.706 & {- 1.881} \\0.386 & {- 4.826} & 23.327\end{pmatrix}$and $M = \begin{pmatrix}33.29 & 14.026 & 2.506 \\13.994 & 35.411 & {- 3.762} \\0.772 & {- 9.652} & 46.655\end{pmatrix}$

-   -   are equivalent in terms of their color calibrating accuracy.

While the method of individually calibrating each imager device byexposing that device to the target chips of a rendition chart isfundamentally correct in its approach, it is cumbersome to implement inhigh volume production. For example, multiple color targets, typicallytwenty-four, are required to accumulate the tested imager device'sresponse to the Macbeth Colorchecker®. In other words, twenty-four colortargets are imaged sequentially for each imager device being calibrated.This technique requires substantial amount of time which hinders theflow of production thereby increasing the production cost. Generally,each imager device produced during manufacture is presumed to have itsown color calibrating matrix corresponding to the variation in RGBresponses and thus, each imager device is calibrated individually. Inaddition, because the targets are changed frequently during calibration,the targets are subject to possible contamination during handling whichresults in an inaccurate calibration. Further, the targets may fade withconstant exposure to light requiring special storage during non-use andfrequent change out. Additionally, because the color of the reflectivecolor targets varies with the ruminating light, a reference light sourcecorresponding to CIE D65 illumination is provided that needs to beconstantly checked for color temperature and intensity. Furthermore, inusing color targets, a fairly large production area must be allocated sothat an appropriate target distant relationship exists with the imagesensor under calibration. Therefore, what is needed is a method andapparatus for producing the color calibration coefficients or colorcalibrating matrix without the difficulties associated with the use ofreflective color targets.

BRIEF SUMMARY OF THE INVENTION

A method and apparatus for color calibrating an imager device isdisclosed. The imager device is subjected to a plurality of lightsources. Color channel responses are obtained from the imager device andthe color calibrating coefficients are determined.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects, features and advantage of the method and apparatus for thepresent invention will be apparent from the following description inwhich:

FIG. 1 illustrates the spectral sensitivity corresponding to the humaneye in terms of XYZ tristimulus values;

FIG. 2 illustrates an example of a red, blue and green (RGB) response ofan imager device;

FIG. 3 depicts an exemplary embodiment of the present inventionillustrating the calibration instrument;

FIG. 4 illustrates an exemplary embodiment of the present invention;

FIG. 5 illustrates an exemplary embodiment of the present invention thatuses statistical correlation;

FIG. 6 illustrates an exemplary table used for correlating the imagerdevices' responses;

FIG. 7 illustrates an exemplary embodiment of the present invention thatuses sets of weighting factors;

FIG. 8 illustrates another exemplary embodiment of the present inventionusing sets of weighting factors; and

FIG. 9 illustrates target color chips of a Macbeth Colorchecker® colorrendition chart.

DETAILED DESCRIPTION OF THE INVENTION

The present invention uses a set of light emitting diodes (LEDs) orother light sources to provide a stimuli for the imager device toproduce a color calibration matrix. In so providing, many of thedisadvantages of using reflective color targets are overcome. It will beappreciated that one characteristic feature of LEDs is that LEDs have ahigh degree of light output stability. It will also be appreciated thatthe light sources will be understood to mean originating or radiatinglight sources. It will further be appreciated that the present inventioncan be practiced with both Complementary Metal Oxide Semiconductor(CMOS) devices and Charge-Coupled Device (CCD) devices as well as otherimager devices. It will further be appreciated that while the exemplaryembodiment is described in terms of red, green and blue (RGB) response,it should by no means be construed as a limitation. Other color systemsare equally applicable, for example, cyan magenta yellow (CMY) colorsystem and cyan, magenta, yellow, green (CMYG) color system amongothers. Accordingly, the responses from the various color systems willbe collectively referred to as color channel responses. Furthermore, itwill be appreciated that while the exemplary embodiment is described interms of 3×3 matrix, other matrices may be used, for example, 3×n matrixor m×n matrix, where m, n are integers, depending on the nature of thecolor calibration.

FIG. 3 illustrates an exemplary embodiment of the invention. Thecalibration instrument 10 comprises a chamber 12 with an aperture 16 toallow an imager device 18 to be calibrated by its access to the interiorof the chamber 12. Within the chamber 12 are incorporated a plurality ofLEDs or other light radiation sources 14 that provide the stimuli forthe imager device 18. The LEDs or other light radiation sources 14 maybe controlled by a computer 20 according to the exemplary methods to bedescribed. The computer 20 may further receive a first set of RGBoutputs from the imager device 18 and using those output values, run acolor calibration program to produce a 3×3 color calibrating matrix forthe imager device 18. The produced 3×3 color calibrating matrix may bestored in a memory device such as read only memory (ROM) within theimager device 18 and is subsequently used to map the read RGB valuesinto corresponding XYZ tristimulus values. By using the calibrationinstrument 10 to calibrate the various imager devices, reflective colortargets are no longer needed. Specifically, by using the LEDs or otherlight sources 14, the same calibration result can be obtained as wouldhave been with the color targets. Generally, five LEDs are used asindicated by the “5” marked onto the communication line between computer20 and light radiation sources 14, although more than five LEDs or aslow as three LEDs may be used depending on the color region to becovered. In using five LEDs, peak emission wavelengths at 430, 470, 545,590 and 660 nm are used to provide the stimuli that gives the result aswould be obtained by means of calibration with reflective color targetscorresponding to the Macbeth Colorchecker® targets. However, it shouldbe noted that other peak wavelengths may be used depending on theparticular desired results to be achieved. In this instance, theparticular peak wavelengths have been chosen to meet the wavelengths ofLEDs that are commercially available while also providing strongcorrelation with the color coefficients of the color calibrating matrix.The following list specifies diode center wavelengths (in nm) andmanufacturer's names:

-   -   430 nm Cree Research, Durham, N.C.    -   450 nm Nichia America Corp., Mountville, Pa.    -   470 nm Micro Electronics Corp., Santa Clara, Calif.    -   481 nm Hewlett-Packard, Palo Alto, Calif.    -   544 nm Toshiba American Electronics Components, Inc., Irvine,        Calif.    -   562 nm Toshiba American Electronics Components, Inc., Irvine,        Calif.    -   590 nm Toshiba American Electronics Components, Inc., Irvine,        Calif.    -   592 nm Hewlett-Packard, Palo Alto, Calif.    -   612 nm Toshiba American Electronics Components, Inc., Irvine,        Calif.    -   615 nm Hewlett-Packard, Palo Alto, Calif.    -   637 nm Hewlett-Packard, Palo Alto, Calif.    -   644 nm Hewlett-Packard, Palo Alto, Calif., Toshiba American        Electronics Components, Inc., Irvine, Calif.    -   660 nm Toshiba American Electronics Components, Inc., Irvine,        Calif.

It should be noted that better correlation with the coefficients of thecolor calibrating matrix may be obtained by using LEDs with band spreadsthat have wide-bands (i.e., peak wavelength±50 nm nanometers) as opposedto LEDs with narrow-bands (i.e., wavelength±5 nm).

As to the remaining figures, various exemplary methods for producing 3×3color calibrating matrix will now be described in terms of a five LEDset, which should not be construed as limitations.

FIG. 4 illustrates an exemplary embodiment of the present invention. Inthis example, the color calibration to produce the 3×3 color calibratingmatrix is directly applied to the RGB values produced by the five LEDs.By applying directly, there is a presumption that the lights of the LEDsare sufficient to define the colors in the various regions of the colorspace. Therefore, the embodiment does not calibrate by correlating withthe Macbeth Colorchecker® targets and may be sufficient to provideadequate color accuracy, depending upon the calibration requirements.The method is as follows:

Block 41 illustrates the steps of determining the XYZ tristimulus valuesof the LEDs. This may be done through the use of a spectrophotometer. (Aspectrophotometer may be viewed as an instrument used to determine theintensity of various wavelengths in a spectrum of light.) Let the fiveLEDs be represented by:

-   -   X_(D1), Y_(D1), Z_(D1) is the XYZ Tristimulus Value for LED#1    -   X_(D2), Y_(D2), Z_(D2) is the XYZ Tristimulus Value for LED#2    -   X_(D3), Y_(D3), Z_(D3) is the XYZ Tristimulus Value for LED#3    -   X_(D4), Y_(D4), Z_(D4) is the XYZ Tristimulus Value for LED#4    -   X_(D5), Y_(D5), Z_(D5) is the XYZ Tristimulus Value for LED#5

Block 42 illustrates the imager device to be calibrated beingilluminated by the five LEDs sequentially and the RGB responsesrecorded. Let the RGB responses recorded be:

-   -   R_(D1), G_(D1), B_(D1) is the imager RGB response to LED#1    -   R_(D2), G_(D2), B_(D2) is the imager RGB response to LED#2    -   R_(D3), G_(D3), B_(D3) is the imager RGB response to LED#3    -   R_(D4), G_(D4), B_(D4) is the imager RGB response to LED#4    -   R_(D5), G_(D5), B_(D5) is the imager RGB response to LED#5

Block 43 illustrates the recorded RGB responses being loaded into a MEASmatrix: ${MEAS} = \begin{bmatrix}R_{D1} & G_{D1} & B_{D1} \\R_{D2} & G_{D2} & B_{D2} \\R_{D3} & G_{D3} & B_{D3} \\R_{D4} & G_{D4} & B_{D4} \\R_{D5} & G_{D5} & B_{D5}\end{bmatrix}$

Block 44 illustrates the color calibrating coefficients (i.e. M₁₁, . . ., M₃₃) of the 3×3 matrix are determined by: $\begin{bmatrix}M_{11} \\M_{12} \\M_{13}\end{bmatrix} = {{\left( {{MEAS}^{T} \cdot {MEAS}} \right)^{- 1} \cdot {{{MEAS}^{T}\begin{bmatrix}X_{D1} \\X_{D2} \\\vdots \\X_{D5}\end{bmatrix}}\begin{bmatrix}M_{21} \\M_{22} \\M_{23}\end{bmatrix}}} = {{\left( {{MEAS}^{T} \cdot {MEAS}} \right)^{- 1} \cdot {{{MEAS}^{T}\begin{bmatrix}Y_{D1} \\Y_{D2} \\\vdots \\Y_{D5}\end{bmatrix}}\begin{bmatrix}M_{31} \\M_{32} \\M_{33}\end{bmatrix}}} = {\left( {{MEAS}^{T} \cdot {MEAS}} \right)^{- 1} \cdot {{MEAS}^{T}\begin{bmatrix}Z_{D1} \\Z_{D2} \\\vdots \\Z_{D5}\end{bmatrix}}}}}$

FIG. 5 illustrates another exemplary embodiment of the presentinvention. This example may include Macbeth Colorchecker® simulationthrough statistical correlation with LED responses. To aid in theunderstanding of this exemplary method, FIG. 6 will be used. FIG. 6illustrates table 60 showing a plurality (N_(ID)) of tested imagerdevices 61 having imager device responses 65 to the twenty-fourreflective color target chips of the Macbeth Colorchecker® renditionchart. Imager device responses 65 may be RGB responses. The MacbethColorchecker® reflective color target chips are defined by the colorcalibrating coefficients M₁₁, . . . M₃₃ of the 3×3 matrix coefficients63. The 3×3 matrix coefficients 63 are plotted with the correspondingimager device responses 65 to the five LEDs 14 of FIG. 3. Once asufficient quantity of imager devices 61 are calibrated, the accumulateddata (63 and 65) may then be used to determine the statisticalcorrelation between the imager device responses 65 and the 3×3 matrixcoefficients 63.

FIG. 5 will now illustrate the procedure in more detail. Block 51illustrates an imager device to be calibrated being exposed totwenty-four reflective color targets corresponding to the MacbethColorchecker®. FIG. 9 illustrates target color chips of a MacbethColorchecker® color rendition chart. However, other color targets may beused provided the XYZ tristimulus values of the targets are known.Further, the number of targets may be varied according to a desiredresult. Block 52 illustrates a 3×3 color calibrating matrix beingconstructed from the stored or recorded RGB values of the twenty-fourtargets. This procedure has been previously described in the BackgroundInformation section above. Let the 3×3 matrix resulting from the colorcalibration using the color targets be represented by:$M_{3 \times 3} = \begin{matrix}M_{11} & M_{12} & M_{13} \\M_{21} & M_{22} & M_{23} \\M_{31} & M_{32} & M_{33}\end{matrix}$

Where M₁₁, . . . , M₃₃ are the color calibrating coefficients of thecolor calibrating matrix.

Block 53 illustrates the same imager device being stimulated by a seriesof five LEDs and the RGB responses for the five LEDs recorded. Theimager device under test is illuminated sequentially by all five LEDsand a total of fifteen responses (five LEDs multiplied by three RGBcolors) are recorded. Taking the five LEDs employed to be LED#1–LED#5,let R_(D1) represent the imager's red channel response to LED#1.Similarly, let G_(D1) represent the imager's green channel response toLED#1 and so forth. The imager device responses can be represented as:

-   -   R_(D1), G_(D1), B_(D1) is the imager RGB response to LED#1    -   R_(D2), G_(D2), B_(D2) is the imager RGB response to LED#2    -   R_(D3), G_(D3), B_(D3) is the imager RGB response to LED#3    -   R_(D4), G_(D4), B_(D4) is the imager RGB response to LED#4    -   R_(D5), G_(D5), B_(D5) is the imager RGB response to LED#5

Block 54 illustrates blocks 51 to 53 being repeated until a desirednumber of imager devices have been calibrated. From the combinedaccumulated data, a table such as the one illustrated in FIG. 6 may beconstructed. Blocks 55 to 56 illustrate the steps that once enough datahas been accumulated, polynomial regression may be used to determine thecorrelation between the statistical correlation between the 3×3 matrixcoefficients 63 and the imager device responses 65. Polynomialregression is based on the theory that, through the use of simultaneousequations, a correlation between measured variable responses can beapproximated. Polynomial regression is well known in linear algebra,however, further discussion of the polynomial regression method in thecontext of imager devices may be found in Henry R. Kang, “ColorTechnology for Electronic Imaging Devices” (SPIE Optical EngineeringPress) at pages 55–62. In summary, using data obtained from multipleimager devices, statistical regression is used to find the correlationbetween the imager devices' responses 65 to LEDs and the coefficients 63of the 3×3 matrix obtained from of the same imager device using colortargets. The net result is a set of equations of the form:M ₁₁ =P ₀ +P ₁ *R _(D1) +P ₂ *G _(D1) +P ₃ *B _(D1) +P ₄ *R _(D2) +P ₅*G _(D2) +P ₆ *B _(D2) +P ₇ *R _(D3) +P ₈ *G _(D3) +P ₉ *B _(D3) +P ₁₀*R _(D4) +P ₁₁ *G _(D4) +P ₁₂ *B _(D4) +P ₁₃ *R _(D5) +P ₁₄ *G _(D5) +P₁₅ *B _(D5)

-   -   where the values P₀, . . . , P₁₅ represent the correlation        coefficients to be statistically determined. The correlation        coefficients may be determined through well known statistical        methods or alternatively, by using a statistics analysis program        such as JMP commercially available from SAS Institute, Inc.,        Cary, N.C. In any event, a different set of correlation        coefficients must be determined for each color calibrating        coefficient of the color calibration matrix (i.e. M₁₁, M₁₂ . . .        M₃₃) which is represented by blocks 57 to 58. Block 59        illustrates that once the set of equations correlating the        calibrating coefficients of the 3×3 matrix 63 and the imager        device response to five LEDs 65 is obtained, the color targets        are no longer necessary and the set of equations is used for        subsequent color calibration of the imager devices. The        advantage of this approach is that the color calibration        coefficients are determined through indirect comparison with a        “golden standard” without the continuing use of the Macbeth        Colorchecker®.

FIG. 7 illustrates another embodiment of the present invention. Thisexample involves the simulation of colors of the Macbeth Colorchecker®through a combination of LEDs lighted simultaneously. In other words, byusing the LED lights as the basis, a combination of the LED lightspowered simultaneously according to sets of weighting factors give thesame color characteristics as the Macbeth Colorchecker® targets understandard CIE D65 illumination. The simulated colors are presented one ata time to the imager device and the associated RGB responses arerecorded. The color calibration is then performed in a similar manner asthat performed when using color target. This color calibration procedurehas been described in the Background Information section above. FIG. 7illustrates the exemplary method in more detail. Block 71 illustratesthe step of determining the XYZ tristimulus values of the LEDs. This maybe done through the use of a spectrophotometer. Let the five LEDs berepresented as:

-   -   X_(D1), Y_(D1), Z_(D1) is the XYZ Tristimulus Value for LED#1    -   X_(D2), Y_(D2), Z_(D2) is the XYZ Tristimulus Value for LED#2    -   X_(D3), Y_(D3), Z_(D3) is the XYZ Tristimulus Value for LED#3    -   X_(D4), Y_(D4), Z_(D4) is the XYZ Tristimulus Value for LED#4    -   X_(D5), Y_(D5), Z_(D5) is the XYZ Tristimulus Value for LED#5

Block 72 illustrates the step of determining the XYZ tristimulus valuesof the Macbeth colors to be simulated that are represented as:

-   -   X_(Mac1), Y_(Mac1), Z_(Mac1) is the XYZ Tristimulus Value for        Macbeth Color#1    -   X_(Mac2), Y_(Mac2), Z_(Mac2) is the XYZ Tristimulus Value for        Macbeth Color#2        -   :        -   :    -   X_(Mac24), Y_(Mac24), is the Z_(Mac24)—XYZ Tristimulus Value for        Macbeth Color#24

Block 73 illustrates the step of determining a set of weighting factorsthat is applied to the LEDs to allow simulation of the Macbeth color.The relationship can be expressed as: $\begin{bmatrix}X_{Mac1} \\Y_{Mac1} \\Z_{Mac1}\end{bmatrix} = {\begin{bmatrix}X_{D1} & X_{D2} & X_{D3} & X_{D4} & X_{D5} \\Y_{D1} & Y_{D2} & Y_{D3} & Y_{D4} & Y_{D5} \\Z_{D1} & Z_{D2} & Z_{D3} & Z_{D4} & Z_{D5}\end{bmatrix}\begin{bmatrix}f_{1,1} \\f_{1,2} \\f_{1,3} \\f_{1,4} \\f_{1,5}\end{bmatrix}}$

Where (f_(1,1), . . . f_(1,5)) is the set of weighing factors.

The above relationship can be rewritten as: $\begin{bmatrix}X_{Mac1} \\Y_{Mac1} \\Z_{Mac1}\end{bmatrix} = {\left\lbrack M_{LED} \right\rbrack\begin{bmatrix}f_{1,1} \\f_{1,2} \\f_{1,3} \\f_{1,4} \\f_{1,5}\end{bmatrix}}$A similar expression can be written for each Macbeth color:$\begin{bmatrix}X_{Mac2} \\Y_{Mac2} \\Z_{Mac2}\end{bmatrix} = {{\left\lbrack M_{LED} \right\rbrack\begin{bmatrix}f_{2,1} \\f_{2,2} \\f_{2,3} \\f_{2,4} \\f_{2,5}\end{bmatrix}}\mspace{14mu}\left( {{etc}.} \right)}$

In the above expressions, the first subscript on the weighting factor frefers to the Macbeth color being matched (i.e., 1–24). The secondsubscript refers to the LED (i.e., 1–5) associated with the weightingfactor.

The above relationship can be rewritten to determine the set ofweighting factors required for simulation as: $\begin{bmatrix}f_{1,1} \\f_{1,2} \\f_{1,3} \\f_{1,4} \\f_{1,5}\end{bmatrix} = {{\left( {\left\lbrack M_{LED} \right\rbrack^{T}\left\lbrack M_{LED} \right\rbrack} \right)^{- 1}\left\lbrack M_{LED} \right\rbrack}^{T}\begin{bmatrix}X_{Mac1} \\Y_{Mac1} \\Z_{Mac1}\end{bmatrix}}$

Where [M_(LED)]^(T) is the transpose matrix of [M_(LED)] The five LEDsselected should have the basis which can describe all of the colors ofthe Macbeth Colorchecker®. However, if this condition is not metexactly, substitute synthesizable colors may be used which are closeapproximations to the Macbeth colors. Alternately, different lightsources could be selected to better span the required color space. Inthis instance, the five LEDs have peak wavelengths at 430, 470, 545, 590and 660 nm respectively.

Block 74 illustrates storing the obtained set of weight factors fromabove. Block 75 illustrates blocks 71 to 74 being repeated to find theset of weighting factors for each of the Macbeth colors to be simulated.Blocks 76 to 78 illustrate that once the twenty-four sets of weightingfactors have been stored corresponding to the respective Macbeth colors,the five LEDs are simultaneously illuminated with the drive power in theproportions indicated by the weighting factors. An image of the color iscaptured by the tested imager device and the RGB responses recorded. Intotal, twenty-four images are captured to accumulate the total systemresponse to the twenty-four colors of the Macbeth Colorchecker®. Block79 illustrates the responses are then used by the color calibrationprocedure which has been described in the background information toproduce the 3×3 color calibrating matrix 63.

The advantage to this approach is that the equivalent Macbeth colors aredirectly synthesized and may therefore be directly measured by aspectrophotometer to determine the accuracy of the color rendition. Thiswould provide a convenient method of verifying that the calibrationinstrument is itself in calibration (i.e., it provides a method ofcalibration traceability).

FIG. 8 illustrates another embodiment of the present invention. In thisexemplary method, rather than synthesizing the Macbeth colors with LEDs,a knowledge of the system responses to the LED stimulus is employed todetermine and predict what the system response would be to the standardMacbeth colors. These predictions are then used to provide the responsedata required in the color calibration to produce the 3×3 colorcalibrating matrix. The method is premised on linearity of systemresponse, and on the presumption that the LEDs have the basis that candescribe all of the colors of the Macbeth Colorchecker®. If thispresumption is not met exactly, substitute colors may be used.

Block 81 illustrates the step of determining the intercept of the testedimager device's RGB responses for zero input. This step is performed todetermine the offsets of the imager device to be calibrated. The purposeis to allow more accurate linear interpolation of results. As anexample, for an imager device with positive offsets, the correction foroffset may be an essentially equivalent to a dark frame subtraction(i.e., offset corresponding to the imager device's response to thedark).

We will term these offsets R₀, G₀, B₀. For example:

Block 82 illustrates the step of illuminating the imager device witheach of the five LEDs and recording the imager responses for each LED.Let the imager device responses to the LEDs be represented by:

-   -   R_(D1), G_(D1), B_(D1) is the imager RGB response to LED#1    -   R_(D2), G_(D2), B_(D2) is the imager RGB response to LED#2    -   R_(D3), G_(D3), B_(D3) is the imager RGB response to LED#3    -   R_(D4), G_(D4), B_(D4) is the imager RGB response to LED#4    -   R_(D5), G_(D5), B_(D5) is the imager RGB response to LED#5

Block 83 illustrates storing the above imager device responses to thefive LEDs.

Block 84 illustrates the step of computing the set of weighting factorsassociated with each of the twenty-four Macbeth colors. The procedurefor determining the set of weighting factors has been described withrespect to FIG. 7.

Block 85 illustrates applying the computed sets of weighting factors tothe imager device's RGB responses to the five LEDs to determine theequivalent Macbeth color response:

For example: $\begin{matrix}\begin{matrix}{R_{1} = {{f_{1.1}\left( {R_{D1} - R_{0}} \right)} + R_{0} +}} \\{{f_{1.2}\left( {R_{D2} - R_{0}} \right)} + R_{0} +} \\{{f_{1.3}\left( {R_{D3} - R_{0}} \right)} + R_{0} +} \\{{f_{1.4}\left( {R_{D4} - R_{0}} \right)} + R_{0} +} \\{{f_{1.5}\left( {R_{D5} - R_{0}} \right)} + R_{0}}\end{matrix} & \begin{matrix}{G_{1} = {{f_{1.1}\left( {G_{D1} - G_{0}} \right)} + G_{0} +}} \\{{f_{1.2}\left( {G_{D2} - G_{0}} \right)} + G_{0} +} \\{{f_{1.3}\left( {G_{D3} - G_{0}} \right)} + G_{0} +} \\{{f_{1.4}\left( {G_{D4} - G_{0}} \right)} + G_{0} +} \\{{f_{1.5}\left( {G_{D5} - G_{0}} \right)} + G_{0}}\end{matrix} & \begin{matrix}{B_{1} = {{f_{1.1}\left( {B_{D1} - B_{0}} \right)} + B_{0} +}} \\{{f_{1.2}\left( {B_{D2} - B_{0}} \right)} + B_{0} +} \\{{f_{1.3}\left( {B_{D3} - B_{0}} \right)} + B_{0} +} \\{{f_{1.4}\left( {B_{D4} - B_{0}} \right)} + B_{0} +} \\{{f_{1.5}\left( {B_{D5} - B_{0}} \right)} + B_{0}}\end{matrix} \\\vdots & \vdots & \vdots \\\begin{matrix}{R_{24} = {{f_{24.1}\left( {R_{D1} - R_{0}} \right)} + R_{0} +}} \\{{f_{24.2}\left( {R_{D2} - R_{0}} \right)} + R_{0} +} \\{{f_{24.3}\left( {R_{D3} - R_{0}} \right)} + R_{0} +} \\{{f_{24.4}\left( {R_{D4} - R_{0}} \right)} + R_{0} +} \\{{f_{24.5}\left( {R_{D5} - R_{0}} \right)} + R_{0}}\end{matrix} & \begin{matrix}{G_{24} = {{f_{24.1}\left( {G_{D1} - G_{0}} \right)} + G_{0} +}} \\{{f_{24.2}\left( {G_{D2} - G_{0}} \right)} + G_{0} +} \\{{f_{24.3}\left( {G_{D3} - G_{0}} \right)} + G_{0} +} \\{{f_{24.4}\left( {G_{D4} - G_{0}} \right)} + G_{0} +} \\{{f_{24.5}\left( {G_{D5} - G_{0}} \right)} + G_{0}}\end{matrix} & \begin{matrix}{B_{24} = {{f_{24.1}\left( {B_{D1} - B_{0}} \right)} + B_{0} +}} \\{{f_{24.2}\left( {B_{D2} - B_{0}} \right)} + B_{0} +} \\{{f_{24.3}\left( {B_{D3} - B_{0}} \right)} + B_{0} +} \\{{f_{24.4}\left( {B_{D4} - B_{0}} \right)} + B_{0} +} \\{{f_{24.5}\left( {B_{D5} - B_{0}} \right)} + B_{0}}\end{matrix}\end{matrix}$

Block 86 illustrates the use the computed equivalent responses fromabove which is loaded into a MEAS table as described in the BackgroundInformation section above and the color calibration procedure performedto determine the 3×3 color calibration matrix.

This method only requires capturing five frames (i.e., one frame foreach LED) and yet, is capable of determining the color calibrationmatrix as if the calibration had been performed using twenty-fourreflective color targets.

It will however be evident that various modifications and changes can bemade thereto without departing from the broader spirit and scope of theinvention as set forth in the appended claims. The specification anddrawings are, accordingly, to be regarded in an illustrative rather thana restrictive sense. Therefore, the scope of the invention should belimited only by the appended claims.

1. A method to calibrate imager device responses, comprising: presentinga plurality of light radiating sources; producing a first set ofresponses from a spectrophotometer based on the plurality of lightradiating sources; producing a second set of responses from an imager byexposing the imager device to the plurality of light radiating sources;and determining calibrating coefficients from the first set of responsesand the second set of responses.
 2. The method of claim 1, whereinpresenting a plurality of light radiating sources includes presentingthree to more than five light emitting diodes, wherein each lightemitting diode includes a different spectral radiation characteristicwithin the spectral sensitivity of the human visual system.
 3. Themethod of claim 2, wherein presenting three to more than five lightemitting diodes includes presenting five light emitting diodes havingthe peak wavelengths of 430 nm, 470 nm, 545 nm, 590 nm, and 660 nm,respectively.
 4. The method of claim 1 wherein producing the first setof responses includes mapping the first set of responses as red, green,and blue values into a plurality of XYZ tristimulus values.
 5. Themethod of claim 1 wherein producing the first set of responses based onthe plurality of light radiating sources includes exposing aspectrophotometer to the plurality of light radiating sources.
 6. Themethod of claim 1 wherein exposing the imager device to the plurality oflight radiating sources includes illuminating the imager devicesequentially with each of the light radiating sources.
 7. A method tocalibrate an imager device, comprising: (i) presenting a plurality N ofimager devices, where N represents a predetermined number of imagerdevices; (ii) exposing the first (N=1) imager device to a target toproduce a first set of target results; (iii) calculating a first set ofcalibrating coefficients from the first set of target results; (iv)exposing the first imager device to a plurality of light radiationsources to produce a first set of source results, wherein the first setof calibrating coefficients and the first set of source results form apair of results; (v) repeating steps (ii) through (iv) N−1 times byemploying a different imager device during each repeat of steps (ii)through (iv); and (vi) determining the correlation between the pluralityN of imager devices by using each pair results.
 8. The method of claim 7wherein exposing the first (N=1) imager device to a target includespresenting a target that represents the spectral sensitivity of thehuman visual system.
 9. The method of claim 8 wherein presenting atarget that represents the spectral sensitivity of the human visualsystem includes presenting a Macbeth Colorchecker® color renditionchart.
 10. The method of claim 7, each light radiation source having adifferent spectral radiation characteristics, wherein exposing the firstimager device to a plurality of light radiation sources includesradiating a series of lights from the plurality of light radiationsources.
 11. The method of claim 7, wherein exposing the first imagerdevice to a plurality of light radiation sources includes presentingfive light emitting diodes having the peak wavelengths of 430 nm, 470nm, 545 nm, 590 nm, and 660 nm, respectively.
 12. The method of claim 7,wherein determining the correlation between the plurality N of imagerdevices by using each pair results includes employing polynomialregression.
 13. The method of claim 7, wherein determining thecorrelation between the plurality N of imager devices by using each pairresults includes deriving a unique set of correlation coefficients foreach set of calibrating coefficients.
 14. The method of claim 13,wherein deriving a unique set of correlation coefficients for each setof calibrating coefficients includes employing a statistics analysisprogram.
 15. The method of claim 13, further comprising: exposing animager device to light reflecting off of an object to produce a set ofobject responses; and applying the correlation coefficients to the setof object responses to produce the image product.